When you drop a 0.38 kg apple, Earth exerts
a force on it that accelerates it at 9.8 m/s^2
toward the earth’s surface. According to Newton’s third law, the apple must exert an equal
but opposite force on Earth.If the mass of the earth 5.98 × 1024 kg, what
is the magnitude of the earth’s acceleration
toward the apple?
Answer in units of m/s2
Don't understand. Please help
the Earth and the apple attract each other with equal force
because the mass of the Earth is about 25 orders of magnitude greater
... the Earth's acceleration toward the apple is comparably less
a = f / m = (.38 * 9.8) / 5.98E24
Well, of course, Earth is always eager to demonstrate its dancing skills! When you drop an apple and Earth pulls it towards itself, it's like a cosmic waltz between the apple and our lovely planet. According to Newton's third law, for every action, there is an equal and opposite reaction. So, as Earth exerts a force on the apple, the apple reciprocates with an equal but opposite force on Earth.
To determine the magnitude of Earth's acceleration towards the apple, we can use the formula for gravitational force:
F = (m1 * m2) / r^2,
where F is the force, m1 and m2 are the masses of the two objects, and r is the distance between them.
Since the apple's mass is 0.38 kg and Earth's mass is 5.98 × 10^24 kg, we can plug these values into the formula. The distance between the apple and Earth's center is not given, but we usually consider it to be approximately the radius of the Earth, which is 6,371 km (or 6,371,000 m). So, the formula becomes:
F = (0.38 kg * 5.98 × 10^24 kg) / (6,371,000 m)^2.
Simplifying this expression gives us the magnitude of the gravitational force between the apple and Earth.
However, to calculate the acceleration of Earth towards the apple, we need to rearrange Newton's second law:
F = m * a,
where F is the force and m is the mass being accelerated. In this case, the mass being accelerated is Earth (5.98 × 10^24 kg). Solving for a, we get:
a = F / m.
Now we can plug in the gravitational force we calculated earlier and the mass of Earth into this equation to find the acceleration of Earth towards the apple.
To determine the magnitude of the Earth's acceleration toward the apple, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
In this scenario, the force exerted by the apple on the Earth is equal to the force exerted by the Earth on the apple. The mass of the apple is given as 0.38 kg, and the acceleration is 9.8 m/s^2.
To find the acceleration of the Earth toward the apple, we need to rearrange the formula to solve for a:
a = F / m
The force exerted by the apple on the Earth can be calculated as the product of masses of both objects (apple and Earth) and their respective accelerations:
F = (mass of the apple) x (acceleration of the apple)
F = (0.38 kg) x (9.8 m/s^2)
Now, we have the force exerted by the apple on the Earth. To find the acceleration of the Earth toward the apple, we divide this force by the mass of the Earth:
a = F / (mass of the Earth)
a = ((0.38 kg) x (9.8 m/s^2)) / (5.98 x 10^24 kg)
Calculating this expression will give us the magnitude of the Earth's acceleration toward the apple.
To find the magnitude of the Earth's acceleration toward the apple, we can apply Newton's third law of motion. According to the third law, the force exerted by the apple on the Earth is equal in magnitude but opposite in direction to the force exerted by the Earth on the apple.
Given that the mass of the apple is 0.38 kg and it experiences an acceleration of 9.8 m/s² toward the Earth's surface, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a): F = m * a.
Simplifying this equation, we have the force exerted by the apple on the Earth: F(apple on Earth) = (0.38 kg) * (9.8 m/s²).
Now, according to Newton's third law, the force exerted by the Earth on the apple is equal in magnitude but in the opposite direction. Therefore, the force exerted by the Earth on the apple is F(Earth on apple) = - F(apple on Earth).
Since the masses in these equations are constant (0.38 kg for the apple and 5.98 × 10^24 kg for the Earth), we can conclude that the magnitudes of the forces are equal. Thus, F(Earth on apple) = F(apple on Earth).
So, we have:
- F(apple on Earth) = F(Earth on apple)
- (0.38 kg) * (9.8 m/s²) = (5.98 × 10^24 kg) * a, where 'a' represents the acceleration of the Earth toward the apple.
To find 'a', we can rearrange the equation to solve for it:
a = (0.38 kg * 9.8 m/s²) / (5.98 × 10^24 kg)
Calculating this expression, we find:
a ≈ 6.22 × 10^(-23) m/s²
Therefore, the magnitude of the Earth's acceleration toward the apple is approximately 6.22 × 10^(-23) m/s².